pgleissberg {pastecs} | R Documentation

## Gleissberg distribution probability

### Description

The Gleissberg distribution gives the probability to have k extrema in a series of n observations. This distribution is used in the turnogram to determine if monotony indices are significant (see `turnogram()`)

### Usage

    pgleissberg(n, k, lower.tail=TRUE, two.tailed=FALSE)

### Arguments

`n` | the number of observations in the series
`k` | the number of extrema in the series, as calculated by `turnpoints()`
`lower.tail` | if `lower.tail=TRUE` (by default) and `two.tailed=FALSE`, the left-side probability is returned. If it is FALSE, the right-side probability is returned
`two.tailed` | if `two.tailed=TRUE`, the two-sided probability is returned. By default, it is FALSE and a one-sided probability is returned (left or right, depending on the value of `lower.tail`

### Value

a value giving the probability to have `k` extrema in a series of `n` observations

### Note

The Gleissberg distribution is asymptotically normal. For `n` > 50, the distribution is approximated by a Gaussian curve. For lower `n` values, the exact probability is returned (using data in the variable `.gleissberg.table`

### Author(s)

Frédéric Ibanez (ibanez@obs-vlfr.fr), Philippe Grosjean (phgrosjean@sciviews.org)

### References

Dallot, S. & M. Etienne, 1990. Une méthode non paramétrique d'analyse des séries en océanographie biologique: les tournogrammes. Biométrie et océanographie - Société de biométrie, 6, Lille, 26-28 mai 1986. IFREMER, Actes de colloques, 10:13-31.

Johnson, N.L. & Kotz, S., 1969. Discrete distributions. J. Wiley & sons, New York, 328 pp.

### See Also

`.gleissberg.table`, `turnpoints`, `turnogram`

### Examples

    # Until n=50, the exact probability is returned
    pgleissberg(20, 10, lower.tail=TRUE, two.tailed=FALSE)
    # For higher n values, it is approximated by a normal distribution
    pgleissberg(60, 33, lower.tail=TRUE, two.tailed=FALSE)

[Package pastecs version 1.3-2 Index]